We study the approximation of nonsmooth solutions of the transport equation in one space dimension by approximations given by a Runge-Kutta discontinuous Galerkin method of order two. We take an initial datum, which has compact support and is smooth except at a discontinuity, and show that, if the ratio of the time step size to the grid size is less than 1/3, the error at the time T in the L2(ℝ RT)-norm is the optimal order two when DIT is a region of size O(T1/2 h1/2 log 1/h) to the right of the discontinuity and of size O(T1/3 h2/3 log 1/h) to the left. Numerical experiments validating these results are presented.
- Discontinuous Galerkin methods
- Error estimates
- Hyperbolic problems